Problem: Express this quotient in scientific notation: ${\frac{3.760\times 10^{-2}} {4.0\times 10^{-1}}}$
Answer: Start by collecting like terms together. $= {\frac{3.760} {4.0}} \times{\frac{10^{-2}} {10^{-1}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.94 \times 10^{-2\,-\,-1}$ $= 0.94 \times 10^{-1}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.94$ is the same as $9.40 \div 10$ , or $9.40 \times 10^{-1}$ $ = {9.40 \times 10^{-1}} \times 10^{-1} $ $= 9.40\times 10^{-2}$